Perpendicular recording records “magnetic bits” vertically onto the magnetic coating of a disk, rather then horizontally as with conventional longitudinal recording. Actually, there are two basic modes of perpendicular recording. One uses a single pole head for recording onto a double-layer perpendicular medium with a soft underlayer. The second mode uses a conventional longitudinal ring head and a medium without a soft underlayer.
Perpendicular recording has been proved to work at low SNR. However, it has been found that conventional timing recovery method does not work well at low SNR [13-18]. Therefore, practical methods for timing recovery for low SNR become very important as the transition from longitudinal recording towards perpendicular recording progresses.
To the knowledge of the inventors, hitherto no sector-based timing recovery techniques for acquisition and tracking, and no sector-based gain control methods, have been proposed in the magnetic recording literature.
Phase and frequency estimation has previously been used in methods for fast timing acquisition. To shorten the preamble length and to increase the acquisition speed in a data storage system, it is common to estimate the phase and to initiate a phase lock loop from a phase that close to the actual phase of the sampled preamble signal. This is commonly referred to as zero-phase restart. There are several reported studies in this area [1-16].
The methods described in references [5,8] employ an estimation of phase using the following principle: estimate the phase angle τk of the preamble at instants k, by computing, the DFT at a frequency ƒnom, which the frequency of the preamble. For example if the preamble is a sequence y(k) which is the repeating sequence ++−−++−−
  …  ⁢          ,            f      nom        ⁢                  ⁢    is    ⁢                  ⁢          1              4        ⁢        T            where T is the symbol interval. The DFT uses the preamble sequence y(k) to produce an estimate {circumflex over (τ)}k the phase angle τk as follows:
                    τ        ^            k        =                  1                  2          ⁢          π          ⁢                                          ⁢                      f            nom                              ⁢              arctan        ⁡                  (                                    imag              ⁡                              [                                  Y                  ⁡                                      (                                          f                      nom                                        )                                                  ]                                                    real              ⁡                              [                                  Y                  ⁡                                      (                                          f                      nom                                        )                                                  ]                                              )                      ,                where imag[Y(ƒnom)] is the imaginary part of Y(ƒnom), and real[Y(ƒnom)] is the real        part of Y(ƒnom), and        
      Y    ⁡          (              f        nom            )        =            ∑              k        =        1                    length        ⁢                                  ⁢        of        ⁢                                  ⁢        preamble              ⁢                  ⁢                  y        ⁡                  (          k          )                    ⁢              ⅇ                              -            j                    ⁢                                          ⁢          2          ⁢          π          ⁢                                          ⁢                      f            nom                    ⁢          k                    is the DFT of y(k) at ƒnom.
The methods described in references [3, 13-16] employ joint estimation of phase and frequency. They all adopted the following principle:
1. Assume the phase angle τk satisfies: τk=τ0+kΔƒ, where Δƒ=ƒactual−ƒnom.
2. Estimate the phase angle of the preamble at instants k, by computing the DFT at frequency ƒnom using two samples of the preamble sequence y(k) for estimate the τk as follows.
                    τ        ^            k        =                  1                  2          ⁢          π          ⁢                                          ⁢                      f            nom                              ⁢              arctan        ⁡                  (                                    imag              ⁡                              [                                  Y                  ⁡                                      (                                                                  f                        nom                                            ,                      k                                        )                                                  ]                                                    real              ⁡                              [                                  Y                  ⁡                                      (                                                                  f                        nom                                            ,                      k                                        )                                                  ]                                              )                      ,                 where imag[Y(ƒnom,k)] is the imaginary part of Y(ƒnom,k), and real[Y(ƒnom,k)] is the real part of Y(ƒnom,k), and Y(ƒnom,k)=y(k)e−j2πƒnomk+y(k+1)e−j2πƒnomk+1 is the DFT of y(k) at ƒnom calculated using two samples.        3. Using the estimation of the phase angle to do a linear curve fitting to equation τk=τ0+kΔƒ to estimate τ0 and Δƒ.        
It is also known that the best phase can be obtained by minimizing mean square error (MSE) between a predetermined signal and the preamble.